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In this lesson you will learn how to calculate and interpret the quartiles of a dataset.

Quartiles

Now that we've found Q2, we can use that value to help us find Q1 and Q3. Recall our demo dataset:

```tex
c(-108, 4, 8, 15, 16, 23, 42)
```
In this example, Q2 is `15`. To find Q1, we take all of the data points smaller than Q2 and find the median of _those_ points. In this case, the points smaller than Q2 are:

```tex
c(-108, 4, 8)
```
The median of that smaller dataset is `4`. That's Q1!

To find Q3, do the same process using the points that are larger than Q2. We have the following points:

```tex
c(16, 23, 42)
```
The median of _those_ points is `23`. That's Q3! We now have three points that split the original dataset into groups of four equal sizes.


Q1 and Q3


We'll come back to the music dataset in a bit, but let's first practice on a small dataset.

Let's begin by finding the second quartile (Q2). Q2 happens to be exactly the <a href="https://www.codecademy.com/courses/learn-statistics-with-python/lessons/median/exercises/introduction">median</a>. Half of the data falls below Q2 and half of the data falls above Q2.

The first step in finding the quartiles of a dataset is to sort the data from smallest to largest. For example, below is an unsorted dataset:

```tex
c(8, 15, 4, -108, 16, 23, 42)
```

After sorting the dataset, it looks like this:

```tex
c(-108, 4, 8, 15, 16, 23, 42)
```

Now that the list is sorted, we can find Q2. In the example dataset above, Q2 (and the median) is `15` &mdash; there are three points below `15` and three points above `15`.

### Even Number of Datapoints

You might be wondering what happens if there is an even number of points in the dataset. For example, if we remove the `-108` from our dataset, it will now look like this:

```tex
c(4, 8, 15, 16, 23, 42)
```

Q2 now falls somewhere between `15` and `16`. There are a couple of different strategies that you can use to calculate Q2 in this situation. One of the more common ways is to take the average of those two numbers. In this case, that would be `15.5`. 

Recall that you can find the average of two numbers by adding them together and dividing by two.


The Second Quartile

We were able to find quartiles manually by looking at the dataset and finding the correct division points. But that gets much harder when the dataset starts to get bigger. Luckily, there is a function in base R that will find the quartiles for you.

The base R function that we'll be using is named `quantile()`. You can learn more about quantiles in our <a href="https://www.codecademy.com/courses/learn-r/lessons/quantiles-r/exercises/quantiles">quantiles lesson</a>, but for right now all you need to know is that a quartile is a specific kind of quantile.

The code below calculates the third quartile of the given dataset:

```r
dataset <- c(50, 10, 4, -3, 4, -20, 2)
third_quartile <- quantile(dataset, 0.75)
```

The `quantile()` function takes two parameters. The first is the dataset you're interested in. The second is a number between `0` and `1`. Since we calculated the third quartile, we used `0.75` &mdash; we want the point that splits the first 75% of the data from the rest.

For the second quartile, we'd use `0.5`. This will give you the point that 50% of the data is below and 50% is above.

Notice that the dataset doesn't need to be sorted for R's function to work!


Quartiles in R

Great work! You now know how to calculate the quartiles of any dataset by hand and with R. 

Quartiles are some of the most commonly used descriptive statistics. For example, You might see schools or universities think about quartiles when considering which students to accept. Businesses might compare their revenue to other companies by looking at quartiles.

In fact quartiles are so commonly used that the three quartiles, along with the minimum and the maximum values of a dataset, are called the five-number summary of the dataset. These five numbers help you quickly get a sense of the range, centrality, and spread of the dataset.

Quartiles Review

A common way to communicate a high-level overview of a dataset is to find the values that split the data into four groups of equal size.

By doing this, we can then say whether a new datapoint falls in the first, second, third, or fourth quarter of the data.

<img src="https://content.codecademy.com/courses/statistics/quantiles/quartiles.svg" alt = "20 data points, with three lines splitting the data into 4 groups of 5.">

The values that split the data into fourths are the _quartiles_. 

Those values are called the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3)

In the image above, Q1 is `10`, Q2 is `13`, and Q3 is `22`. Those three values split the data into four groups that each contain five datapoints.

In this lesson, you will learn to calculate the quartiles by hand, and by using base R functions.

You just learned a commonly used method to calculate the quartiles of a dataset. However, there is another method that is equally accepted that results in different values! 

Note that there is no universally agreed upon method of calculating quartiles, and as a result, two different tools might report different results.

The second method includes Q2 when trying to calculate Q1 and Q3. Let's take a look at an example:

```tex
c(-108, 4, 8, 15, 16, 23, 42)
```

Using the first method, we found Q1 to be `4`. When looking at all of the points below Q2, we excluded Q2. Using this second method, we _include_ Q2 in each half.

For example, when calculating Q1 using this new method, we would now find the median of this dataset:

```tex
c(-108, 4, 8, 15)
```
Using this method, Q1 is `6`.